Related papers: Convolution of Picard-Fuchs equations
Semigroups, generated by Feller processes killed upon leaving a given domain, are considered. These semigroups correspond to Cauchy-Dirichlet type initial-exterior value problems in this domain for a class of evolution equations with…
We study the local classification of higher order Fuchsian linear differential equations under various refinements of the classical notion of the "type of differential equation" introduced by Frobenius. The main source of difficulties is…
This is a book on derived foliations, that are a generalisation of classical foliations in the context of derived geometry. The text starts with the basic definitions and constructions, then explore foliated cohomology (with crystal…
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…
We focus on Fuchsian equations with four accessory parameters and three singular points. We see that the Fuchsian equations admit a "degeneration scheme" in some sense, which is expected to give rise to a degeneration scheme of discrete…
In [J14], a conjecture was proposed on a relation between the global Arthur parameters and the structure of Fourier coefficients of the automorphic representations in the corresponding global Arthur packets. In this paper, we discuss the…
A class of variable coefficient (1+1)-dimensional nonlinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u^nu_x)_x+h(x)u^m$ is investigated. Different kinds of equivalence groups are constructed including ones with…
We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…
Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in terms of the generators of this algebra.…
The problem of characterizing all new-time transformations preserving the Poisson structure of a finitedimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously…
We compute the local cohomology of vector fields on a manifold. In the smooth case this recovers the diagonal cohomology studied in work of Losik, Guillemin, Fuks and others. In the holomorphic case this cohomology has recently appeared in…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging…
This work provides an effective algorithm for distinguishing finite quotients between two non-isomorphic finitely generated Fuchsian groups $\Gamma$ and $\Lambda$. It will suffice to take a finite quotient which is abelian, dihedral, a…
The main result is an explicit expression for the Pressure Metric on the Hitchin component of surface group representations into PSL(n,R) along the Fuchsian locus. The expression is in terms of a parametrization of the tangent space by…
We introduce the notion of a \emph{conic sequence} of a convex polytope. It is a way of building up a polytope starting from a vertex and attaching faces one by one with certain regulations. We apply this to a toric variety to obtain an…
Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…
The solutions of traditional fractional differential equations neither satisfy group property nor generate dynamical systems, so the study on hyperbolicity is in blank. Relying on the new proposed conformable fractional derivative, we…
We present a simple, but efficient, way to calculate connection matrices between sets of independent local solutions, defined at two neighboring singular points, of Fuchsian differential equations of quite large orders, such as those found…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…